Im doing some basic statistics on a dataset of ours. The data is paired samples from patients in a study where we measure the ratio between component A and B in blood (AB-ratio) on people who have been repositioned between the samples or not. We're looking at if there's any difference between the AB-ratio in sample 1 (AB-ratio1) and the AB-ratio in sample 2 (AB-ratio2) in repositioned patients.
I've been using both the raw variables and log-transformed variables.
AB-ratio = A/B. AB-ratio_LOG = log(A)/log(B).
Visually, when plotting the data it appears as if there is a difference between paired samples for repositioned patients, which is also something we see in other analyses. However, wilcoxon signed rank is not significant for the non-logtransformed data.
wilcox.test(AB-ratio1,AB-ratio2,paired=TRUE) #p=0,155
wilcox.test(AB-ratio1_log,AB-ratio2_log,paired=TRUE) #p=0,0053
Is there any reason why it's wrong of me to use the log-transformed variable in this case?
When I use wilcoxon rank sum to compare repositioned patients with non-repositioned patients, we see that the AB-ratio1-AB-ratio2 (AB difference) is greater in the repositioned patients. I can't for the life of me understand how this can be true if the difference between sample 1 and sample 2 is not statistically significant for the repositioned patients to begin with.
Any thoughts?
Below is examples of our data for the AB-ratio and the AB-ratio_log.
AB-ratio1 <- c(3, 3.98907103825137, 0.267379679144385, 7.07070707070707, 2.20224719101124,
7.33067729083665, 7.15434083601286, 8.22558459422283, 6.31578947368421,
44, 2.12121212121212, 0.32258064516129, 0.789473684210526, 0.836236933797909,
1, 1.34328358208955, 3.78504672897196, 0.350877192982456, 0.411522633744856,
0.9375, 0.651260504201681, 0.888888888888889, 3.98190045248869,
1.85750636132316, 12.4759615384615, 1.61111111111111, 1.70091324200913,
7.85930867192238, 1.14647713226205, 1.66666666666667, 0.857142857142857,
2.16981132075472, 7.13541666666667, 3.00518134715026, 1.31386861313869,
10.7531380753138, 2.8, 1.49425287356322, 3.93225331369661, 7.48344370860927,
33.8805970149254, 14, 3.50649350649351, 82.8260869565217, 33.6546184738956,
6.36655948553055, 0.716049382716049, 0.337078651685393, 1.08225108225108,
0.436781609195402, 3.19105691056911, 1.55844155844156, 0.413533834586466,
0.224358974358974, 0.772797527047913, 0.588235294117647, 0.227149810708491,
0.440087145969499, 0.268041237113402, 13.2407407407407, 14.9002849002849,
0.798816568047337, 4.85775059824515, 0.549450549450549, 56.4285714285714,
19.6899224806202, 30.1672240802676, 10.7155025553663, 7.80487804878049,
0.298507462686567, 4.05405405405405, 0.887096774193548, 1.97916666666667,
2.39910313901345, 1.47169811320755, 7.94847328244275, 2.31301939058172,
12.4, 4.8, 0.688259109311741, 0.545454545454546, 0.431034482758621,
4.42748091603053, 0.536585365853659, 7.22222222222222, 6.39494026704146,
30.7692307692308, 27.5, 2.16216216216216, 1.66666666666667, 0.365853658536585,
0.892857142857143, 0.567375886524823, 0.769230769230769, 0.543478260869565,
1.18852459016393, 1.33333333333333, 3.25301204819277, 3.04498269896194,
7.59825327510917, 0.808854831843338, 4.21052631578947, 0.669344042838019,
2.25)
AB-ratio2 <- c(2.63020833333333, 3.28150134048257, 0.224719101123596, 11.8529411764706,
1.95190947666195, 10.5686032138443, 6.25146886016451, 12.2142857142857,
5.55555555555556, 37.4193548387097, 1.19047619047619, 0.377358490566038,
0.573770491803279, 2.24074074074074, 1.15044247787611, 1.53333333333333,
3.2824427480916, 0.683962264150943, 0.437601296596434, 1.26550868486352,
0.650925335035099, 0.769230769230769, 4.52914798206278, 2.04778156996587,
16.0759493670886, 1.25925925925926, 1.07338444687842, 4.97194163860831,
1.29014697876973, 0.833333333333333, 1.95121951219512, 4.62264150943396,
4.66321243523316, 4.54761904761905, 1.0546875, 11.1444141689373,
3.56120826709062, 1.24768946395564, 5.05494505494506, 7.16245487364621,
49.7560975609756, 10, 3.33333333333333, 74.2696629213483, 30.1492537313433,
13.1, 0.742268041237113, 0.526315789473684, 1.66666666666667,
1.0750382848392, 2.44573082489146, 1.55230596175478, 0.586907449209932,
0.226415094339623, 0.775613886536833, 0.625, 0.252025202520252,
0.409429280397022, 0.582010582010582, 18, 12.2077922077922, 1.33815551537071,
3.69109151717847, 0.703218116805721, 90.3703703703704, 20.2097902097902,
20.2013422818792, 6.44189383070301, 9.44162436548223, 0.27972027972028,
14.0277777777778, 2.8421052631579, 7.18978102189781, 3.41981132075472,
1.46341463414634, 9.408, 1.71561051004637, 16.8269230769231,
3.11111111111111, 0.869565217391304, 0.980392156862745, 1.0752688172043,
4.60136674259681, 0.621359223300971, 6.21315192743764, 7.50713606089439,
32.8571428571429, 45.5555555555556, 2.17877094972067, 0.816326530612245,
0.307692307692308, 0.952380952380952, 0.720720720720721, 0.909090909090909,
0.495049504950495, 1.08786610878661, 1.42857142857143, 4.35897435897436,
4.43425076452599, 3.71428571428571, 0.903286829037598, 2.80155642023346,
0.608695652173913, 1)
AB-ratio1_log <- c(0.403638055400894, 0.437148209069139, 0.16362264070524, 0.519191983969621,
0.428371742074317, 0.545843340288609, 0.552456365100691, 0.571157365005211,
0.32914374710378, 0.589053318117168, 0.240186071294515, 0.0793773482041905,
0.258063512743193, 0.309611441864981, 0.264558297597896, 0.304153290607172,
0.440716550142183, 0.207228886777308, 0.22801864499786, 0.313098028367874,
0.38187909611077, 0.164802893085947, 0.447584506566846, 0.405564574574325,
0.587813920070771, 0.425018874195599, 0.439693366303977, 0.596602138758889,
0.466310333927957, 0.0977629998397715, 0.134625308755078, 0.338291767532061,
0.498849007592011, 0.45010764040709, 0.375477492880011, 0.579336444302945,
0.463651235347023, 0.409445786884048, 0.502188878160711, 0.589513812197819,
0.615781441473649, 0.517860937476932, 0.36829208285206, 0.738680083783224,
0.664948012551219, 0.511192449940337, 0.317398214530725, 0.120808847421222,
0.320363042157243, 0.275683208500602, 0.468012784475757, 0.456500157228622,
0.235349275003681, 0.188043829453275, 0.425096098928288, 0, 0.308196076349175,
0.373885958400978, 0.237730420165906, 0.534368855871642, 0.598089770220198,
0.358677614657448, 0.585033378865562, 0.285244699959532, 0.637817317037343,
0.613349266852348, 0.660282315924171, 0.649077297858263, 0.484674137670135,
0.180831000958413, 0.381760866682434, 0.305481270093249, 0.321111628545901,
0.436489054747789, 0.359705214761306, 0.581759924629659, 0.457486766234792,
0.523355421290559, 0.434022530330872, 0.280112408042444, 0.192545320636957,
0.17197127050856, 0.467251518877352, 0.291022237876291, 0.54149541155591,
0.574213804747546, 0.514479491138187, 0.561154512071733, 0.360924584844037,
0.233243139591273, 0.121906987075809, 0.278344419458757, 0.270573613599501,
0.213460268855334, 0.176338904800588, 0.333318454886268, 0.0947800208214054,
0.410509333808922, 0.435894911897064, 0.513906833723027, 0.424279135076009,
0.444776718754767, 0.348626766665653, 0.264915773678585)
AB-ratio2_log <- c(0.437211291175664, 0.528727230169076, 0.175793351566841, 0.601413281238528,
0.441265005933112, 0.597391374790748, 0.578658962222824, 0.611489963475227,
0.342747472984385, 0.591304531086751, 0.254823861174144, 0.0808291346302037,
0.206809501618146, 0.440112441191784, 0.274838833701293, 0.326077126084049,
0.437837604023091, 0.316032499530038, 0.298805543959273, 0.370783294263807,
0.42023081657227, 0.162018151129826, 0.460943157600411, 0.398075654241726,
0.621773701685931, 0.43928108473945, 0.45394125115874, 0.534640224356411,
0.480810680309223, 0, 0.249970666059141, 0.419892583719806, 0.456006621433278,
0.493383164949647, 0.367868857419249, 0.572160870312266, 0.489772686529065,
0.455716312690764, 0.532637721215994, 0.582814537575913, 0.639293757673882,
0.405067840837091, 0.278094243287903, 0.714085328301486, 0.602536931013287,
0.529317823913941, 0.332135782889205, 0.155137570257304, 0.387266154759708,
0.461617889023837, 0.460356815922014, 0.432394739228309, 0.346847161598818,
0.17592312807406, 0.461057717988708, 0, 0.286809362250303, 0.34941739679272,
0.24351735917341, 0.552988145107735, 0.56151855838931, 0.43028689156432,
0.559032622689634, 0.359654269587009, 0.695755387777684, 0.634224756358327,
0.593926639305472, 0.574091267602098, 0.5284738136703, 0.144888400336269,
0.572492584064002, 0.404882804991899, 0.517033617298075, 0.528438125700113,
0.364130169439247, 0.602405636729704, 0.425143145542352, 0.558381735780625,
0.393006808016238, 0.290843635296205, 0.188525090864674, 0.251985459674052,
0.496579211191557, 0.31944218113231, 0.524875184774422, 0.576922780840938,
0.478622464627184, 0.622793996733921, 0.374116997562905, 0.163151219683511,
0.0789501275027734, 0.323868742586923, 0.223242987451848, 0.247439454144716,
0.174553922897488, 0.323171484177901, 0.0956826906757104, 0.419737503184038,
0.478756261014483, 0.465209440456144, 0.458932506482668, 0.421170218342954,
0.344530453619642, 0.188963415090328)
```